In an AC circuit with V = V 0 cos(ωt) and I = I 0 cos(ωt + φ), the average power is:

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In an AC circuit with V = V₀ cos(ωt) and I = I₀ cos(ωt + φ), the average power is:

Answer: (V₀ I₀/2) cos(φ).

A (V₀ I₀/2) cos(φ)
B V₀ I₀ cos(φ)
C (V₀ I₀/2) sin(φ)
D 0

Correct answer: A. (V₀ I₀/2) cos(φ)

Explanation: Instantaneous power p = VI = V₀ I₀ cos(ωt) cos(ωt + φ). Time average gives: P_avg = (V₀ I₀/2) cos(φ) = V_rms I_rms cos(φ).

In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.

Concept context

AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.

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In an AC circuit with V = V0 cos(ωt) and I = I0 cos(ωt + φ), the average power is:

Concept context

More Alternating Current questions

In an AC circuit with V = V₀ cos(ωt) and I = I₀ cos(ωt + φ), the average power is: